The tubuloglomerular feedback (TGF) is an intrarenal mechanism
that stabilizes renal blood flow, GFR, and the tubular flow
rate. The anatomical basis for TGF is the return of the tubule
(the ascending limb of the loop of Henle (ALH)) to its own glomerulus.
The macula densa, which is the sensor mechanism for the TGF,
is a plaque of specialized epithelial cells in the wall of the
ALH. It is localized at the site where the tubule establishes
contact with the glomerulus. Because of a flow dependency of
NaCl reabsorption in the ALH, a change in tubular flow rate,
elicited for example by a change in the arterial pressure, will
lead to a change in the NaCl concentration of the tubular fluid.
This is sensed by the macula densa, and through unknown mechanisms
results in a change in the hemodynamic resistance of the afferent
arteriole. The dynamic properties of the TGF system has been
characterized in experimental studies in both normo-and hypertensive
rats. In normotensive rats, TGF displays autonomous self-sustained
regular oscillations, whereas in spontaneously hypertensive
rats (SHR) highly irregular, "chaotic" fluctuations are present.
Several attempts has been made to formulate mathematical models
of the TGF system that is able to reproduce both the regular
oscillations, and the irregular fluctuations. However, in most
cases the models have been successful in describing the regular
oscillations, but have failed to reproduce the irregular fluctuations.
It has only been possible to achieve irregular (chaotic) fluctuations
in TGF through nonlinear extensions of the equations that describe
the afferent arteriole. Although physiologically justified,
these extensions has lacked a firm experimental basis. To overcome
the shortcomings of the previous models, we have in the present
work extended a model of the TGF mechanism with a model of the
response of the afferent arteriole. To examine the bifurcation
structure of this highly complex model we have applied one-and
two dimensional continuation techniques. The results show that
a Hopf bifurcation causes the system to perform self-sustained
regular oscillations if the feedback gain is sufficiently strong.
If the feedback gain is increased further, a folded structure
of overlapping sheets of period-doubling cascades appear, leading
ultimately to the appearance of classical chaotic behavior.